The notion of a set of conditions presupposed insofar as utterance is understandable, intrigues me.
A couple of philosophers of language (post-Russell) try to account for empty names in virtue of presupposition failure. Richard Holton (among others) explained this example in a seminar once…
If I am to say something like “The Present King of France is sitting on Alexander’s chair”, then we can legitimately reply something like “Hey wait a minute! There is no King of France!”
We say that “The Present King of France” is a statement to which it sets conditions which cannot be fulfilled; or, that it is strange to understand given our contingencies (i.e. A certain French Revolution…)
A stronger claim to make than the semantic contingent background presuppositions; is to state the metaphysical possibilities of understanding a statement. Kant attempts something similar to this description with the categories of the understanding.
But, if I am to say “The present King of France is sitting on Alexander’s chair”, is it acceptable to ask: “Hey wait a minute! Existence is not a predicate!”?